EIGENVALUES AND POLE FUNCTIONS OF HAMILTONIAN-SYSTEMS WITH EIGENVALUE DEPENDING BOUNDARY-CONDITIONS

This paper consists of two chapters. The first chapter concerns matrix functions belonging to the generalized Nevanlinna class N(kappa)m x m. We present results about the operator representation of such functions. These representations are then used to obtain information about the (generalized) poles of generalized Nevanlinna functions. The second chapter may be viewed as a continuation of our paper [DLS3] and treats Hamiltonian systems of differential equations with boundary conditions depending on the eigenvalue parameter. In particular we study the eigenvalues, both isolated and embedded eigenvalues.